16A-FinalSample4

16A-FinalSample4 - f 00 ( x )) and then Find inection...

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Math 16A, Spring 2010 Final Sample 4 Analyze a function, and sketch the graph of that fct, means extract all the informations we can, by using the technique developed in this class. That’s the road map you may use. Domain x and y intercept Continuity (and classify disc. points) HA and VA derive the fct (find f 0 ( x )) and then Study differentiability Find critical points (keeping in mind the difference between the case f 0 ( c ) = 0 flat tg line, and f 0 ( c ) =undef. vertical tg line cusp or node) Find increasing ( f 0 > 0) and decreasing ( f 0 < 0) interval Individuate rel max and min by using first derivative test derive the fct two times (find
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Unformatted text preview: f 00 ( x )) and then Find inection points Find concave up ( f 00 &gt; 0) and concave down ( f 00 &lt; 0) interval Check that the second derivative tests matches with the rel max and min you found previously Use these info the sketch the graph. 1 1. Analyze the function y = x 2 x 2-1 2. Analyze the function y = x x 2-4 3. Analyze the function y = cos ( x ) + sin ( x ) in the interval I = [0 , 6 ], and nd the abs extrema. 4. Find the slope of the tangent line to function f ( x ) = p cos ( x 2 ) sin 2 ( x x 2 + 1 ) in the point (1 ,f (1)) 2...
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16A-FinalSample4 - f 00 ( x )) and then Find inection...

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